SE-SKOLORNAS 2007 Problem 3

Let $\alpha$ , $\beta$ , $\gamma$ be the angles of a triangle. If $a$ , $b$ , $c$ are the side length of the triangle and $R$ is the circumradius, show that $$\cot \alpha + \cot \beta +\cot \gamma =\frac{R\left(a^2+b^2+c^2\right)}{abc}$$